Two finite linear equations whose coefficient determinant is non-zero.
Simultaneous Equations Calculator
Enter your values below to get the result first, then scroll for the full explanation and guidance.
Solution (x, y)
(3, 1)Unique solution
Solution (x, y): (3, 1) (Unique solution)
Cramer's rule solves the two linear equations when their determinant is non-zero.
Simultaneous-equation result
Cramer's rule solves the two linear equations when their determinant is non-zero.
Result snapshot
A quick visual read of the values behind this result.
Determinant-3
Recommended next checks
- →Substitute x and y into both equations to verify the solution.
- Determinant
- -3
Try different values to compare results.
Solve two simultaneous linear equations in x and y when they have one unique solution.
Solution (x, y)
(3, 1)Unique solution
Solution (x, y): (3, 1) (Unique solution)
Cramer's rule solves the two linear equations when their determinant is non-zero.
Simultaneous-equation result
Cramer's rule solves the two linear equations when their determinant is non-zero.
Result snapshot
A quick visual read of the values behind this result.
Determinant-3
Recommended next checks
- →Substitute x and y into both equations to verify the solution.
- Determinant
- -3
Try different values to compare results.
Table of Contents
Table of Contents
About Simultaneous Equations Calculator
Simultaneous Equations Calculator helps you work through the main numbers for this topic quickly with a simple input flow and an instant result.
Use the calculator result as a practical starting point, then review the explanation and assumptions on the page if you want more context.
Calculation method
Use the non-zero determinant and Cramer's rule for a1x+b1y=c1 and a2x+b2y=c2.
Formula explained
Calculation flow
This calculator is structured for fast UK-focused estimates with clear inputs, repeatable logic, and instant results.
Formula
Input values -> calculation engine -> instant result
How the result is built
1Enter the values requested in the form.
2The calculator applies the configured formula logic.
3The result updates instantly with a breakdown.
4Use the output to compare scenarios quickly.
Example
Example verified by the calculator's linear algebra reference cases.
Assumptions
- Two finite linear equations whose coefficient determinant is non-zero.
Source basis
- UK-focused calculator flow
- Structured input validation
- Instant result breakdowns
FAQ
Common questions
Trust and notes
Assumptions and important notes
This calculator is designed to give a fast estimate using the method shown on the page. Results are most useful when your inputs are accurate and the tool matches your situation.
Use the result as guidance rather than a final diagnosis or professional decision. If the result could affect health, legal, financial, or compliance decisions, verify it with a qualified source where appropriate.
- Two finite linear equations whose coefficient determinant is non-zero.
Method
UK calculator guidance
Last reviewed
April 17, 2026